I can find out the browser version and specific capabilities using the HttpBrowserCapabilities object, but is there a way I can find the Document Mode that the browser is using
No. you cannot determine the document mode via server side code. You can check the compat. mode with the trident value in the user agent, which defaults the document mode. Key word..DEFAULTS..IT CAN STILL BE CHANGED via F12. If a user then changes the document mode again, to something besides what compat. mode changes it to, then you will not be able to see the change.